Subgroups — C₁₁₃×#17469 #43285489

Order 28928.

920 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁₃×#3461	C₂	1	1	yes	maximal, characteristic
2	C₁₁₃×#2988	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#1485	C₂	1	2	yes	maximal, complemented
5	C₁₁₃×#1483	C₂	1	2	yes	maximal, complemented
6	C₁₁₃×#1482	C₂	1	2	yes	maximal, complemented
7	C₁₁₃×#1481	C₂	1	2	yes	maximal, complemented
8	C₁₁₃×#1479	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁₃×#1477	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×Q₈⋊C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#544×C₁₁₃	C₄	1	1	yes	characteristic
13	#542×C₁₁₃	—	2	1	no	—
14	#542×C₁₁₃	C₄	1	2	yes	—
15	#541×C₁₁₃	—	2	1	no	—
16	#541×C₁₁₃	C₄	1	2	yes	—
17	#539×C₁₁₃	—	2	2	no	—
18	#537×C₁₁₃	C₄	1	1	yes	characteristic
19	#536×C₁₁₃	C₄	1	1	yes	characteristic
20	#536×C₁₁₃	C₄	1	1	yes	characteristic
21	#533×C₁₁₃	—	2	1	no	—
22	#533×C₁₁₃	C₂²	1	2	yes	—
23	#529×C₁₁₃	—	2	2	no	—
24	#529×C₁₁₃	—	2	1	no	—
25	#529×C₁₁₃	C₂²	1	2	yes	—
26	C₄×#41×C₁₁₃	C₂²	1	1	yes	characteristic
27	C₄×#41×C₁₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
29	#446×C₁₁₃	—	2	1	no	—
30	C₈×Q₈×C₁₁₃	—	2	1	no	—
31	#436×C₁₁₃	—	2	1	no	—
32	#435×C₁₁₃	—	2	2	no	—
33	C₈×D₄×C₁₁₃	—	2	1	no	—
34	C₈×D₄×C₁₁₃	—	2	2	no	—
35	#431×C₁₁₃	C₂²	1	1	yes	characteristic
36	#431×C₁₁₃	C₂²	1	2	yes	—
37	#431×C₁₁₃	C₂²	1	1	yes	characteristic
38	#431×C₁₁₃	C₂²	1	2	yes	—
39	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
41	C₄×M₁₆×C₁₁₃	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
43	Q₈⋊C₈×C₁₁₃	C₂²	1	2	yes	—
44	Q₈⋊C₈×C₁₁₃	C₂²	1	2	yes	—
45	Q₈⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
46	Q₈⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
47	Q₈⋊C₈×C₁₁₃	C₂²	1	2	yes	—
48	Q₈⋊C₈×C₁₁₃	C₂²	1	2	yes	—
49	Q₈⋊C₈×C₁₁₃	C₂²	1	2	yes	—
50	D₄⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
51	D₄⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
52	D₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
53	C₂×#41×C₁₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×#41×C₁₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×Q₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×M₁₆×C₁₁₃	—	2	2	no	—
57	C₂²×C₈×C₁₁₃	—	2	1	no	—
58	C₂²×C₈×C₁₁₃	—	2	1	no	—
59	C₂²×C₈×C₁₁₃	—	2	2	no	—
60	C₄⋊Q₈×C₁₁₃	—	2	1	no	—
61	C₄⋊Q₈×C₁₁₃	—	2	1	no	—
62	C₄⋊Q₈×C₁₁₃	C₂×C₄	1	2	yes	—
63	C₄⋊Q₈×C₁₁₃	C₂×C₄	1	2	yes	—
64	#126×C₁₁₃	—	2	2	no	—
65	#126×C₁₁₃	—	2	2	no	—
66	#126×C₁₁₃	—	2	2	no	—
67	#126×C₁₁₃	—	2	2	no	—
68	#125×C₁₁₃	—	2	2	no	—
69	#125×C₁₁₃	—	2	1	no	—
70	#125×C₁₁₃	—	2	2	no	—
71	#125×C₁₁₃	—	2	2	no	—
72	#125×C₁₁₃	C₂×C₄	1	2	yes	—
73	#124×C₁₁₃	—	2	1	no	—
74	#124×C₁₁₃	—	2	2	no	—
75	#124×C₁₁₃	C₂×C₄	1	2	yes	—
76	#123×C₁₁₃	—	2	2	no	—
77	#123×C₁₁₃	—	2	2	no	—
78	#123×C₁₁₃	—	2	2	no	—
79	#123×C₁₁₃	—	2	2	no	—
80	C₂²⋊Q₈×C₁₁₃	—	2	1	no	—
81	C₂²⋊Q₈×C₁₁₃	—	2	2	no	—
82	C₂²⋊Q₈×C₁₁₃	—	2	1	no	—
83	C₂²⋊Q₈×C₁₁₃	—	2	1	no	—
84	C₂²⋊Q₈×C₁₁₃	—	2	2	no	—
85	C₂²⋊Q₈×C₁₁₃	—	2	2	no	—
86	C₂²⋊Q₈×C₁₁₃	C₂×C₄	1	2	yes	—
87	C₂²⋊Q₈×C₁₁₃	C₂×C₄	1	2	yes	—
88	C₂²⋊Q₈×C₁₁₃	C₂×C₄	1	2	yes	—
89	#121×C₁₁₃	—	2	2	no	—
90	#121×C₁₁₃	—	2	1	no	—
91	#121×C₁₁₃	C₂×C₄	1	2	yes	—
92	C₄×Q₈×C₁₁₃	—	2	1	no	—
93	C₄×Q₈×C₁₁₃	—	2	1	no	—
94	C₄×Q₈×C₁₁₃	—	2	2	no	—
95	C₄×Q₈×C₁₁₃	C₂×C₄	1	2	yes	—
96	C₄×Q₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
97	C₄×Q₈×C₁₁₃	D₄	1	1	yes	characteristic
98	C₄×Q₈×C₁₁₃	D₄	1	1	yes	characteristic
99	C₄×Q₈×C₁₁₃	C₂³	1	2	yes	—
100	C₄×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₁₃	—	2	1	no	—
102	C₄×D₄×C₁₁₃	—	2	1	no	—
103	C₄×D₄×C₁₁₃	—	2	2	no	—
104	C₄×D₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₁₁₃	D₄	1	1	yes	characteristic
106	C₄×D₄×C₁₁₃	D₄	1	2	yes	—
107	C₄×D₄×C₁₁₃	D₄	1	2	yes	—
108	C₄×D₄×C₁₁₃	D₄	1	1	yes	characteristic
109	C₄×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
110	#117×C₁₁₃	—	2	2	no	—
111	#117×C₁₁₃	—	2	1	no	—
112	#117×C₁₁₃	—	2	2	no	—
113	#117×C₁₁₃	C₂×C₄	1	1	yes	characteristic
114	#117×C₁₁₃	C₂×C₄	1	1	yes	characteristic
115	#117×C₁₁₃	C₂×C₄	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
117	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
118	C₂×C₄²×C₁₁₃	—	2	1	no	—
119	C₂×C₄²×C₁₁₃	—	2	1	no	—
120	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
122	C₄⋊C₈×C₁₁₃	—	2	1	no	—
123	C₄⋊C₈×C₁₁₃	—	2	2	no	—
124	C₄⋊C₈×C₁₁₃	—	2	2	no	—
125	C₄⋊C₈×C₁₁₃	—	2	1	no	—
126	C₄⋊C₈×C₁₁₃	C₂³	1	1	yes	characteristic
127	C₄⋊C₈×C₁₁₃	C₂³	1	2	yes	—
128	C₄⋊C₈×C₁₁₃	C₂³	1	1	yes	characteristic
129	C₂²⋊C₈×C₁₁₃	—	2	1	no	—
130	C₂²⋊C₈×C₁₁₃	—	2	2	no	—
131	C₂²⋊C₈×C₁₁₃	—	2	1	no	—
132	C₂²⋊C₈×C₁₁₃	—	2	2	no	—
133	#97×C₁₁₃	—	2	2	no	—
134	C₄×C₈×C₁₁₃	—	2	1	no	—
135	C₄×C₈×C₁₁₃	—	2	1	no	—
136	C₄×C₈×C₁₁₃	—	2	2	no	—
137	C₄×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₁₁₃	C₂³	1	2	yes	—
140	#41×C₁₁₃	—	2	4	no	—
141	#41×C₁₁₃	—	2	4	no	—
142	C₂×Q₈×C₁₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₁₃	—	2	2	no	—
144	C₂×Q₈×C₁₁₃	—	2	4	no	—
145	C₂×Q₈×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×Q₈×C₁₁₃	C₂²×C₄	1	2	yes	—
147	C₂×Q₈×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₁₁₃	—	2	1	no	—
149	C₂×D₄×C₁₁₃	—	2	2	no	—
150	C₂×D₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
151	C₂×D₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
152	C₂×D₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
159	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
164	M₁₆×C₁₁₃	—	4	4	no	—
165	C₂×C₈×C₁₁₃	—	2	1	no	—
166	C₂×C₈×C₁₁₃	—	2	1	no	—
167	C₂×C₈×C₁₁₃	—	2	2	no	—
168	C₂×C₈×C₁₁₃	—	2	1	no	—
169	C₂×C₈×C₁₁₃	—	2	1	no	—
170	C₂×C₈×C₁₁₃	—	2	2	no	—
171	C₂×C₈×C₁₁₃	—	4	2	no	—
172	C₂×C₈×C₁₁₃	—	8	1	no	—
173	C₂×C₈×C₁₁₃	—	8	2	no	—
174	C₄⋊C₄×C₁₁₃	—	2	2	no	—
175	C₄⋊C₄×C₁₁₃	—	2	1	no	—
176	C₄⋊C₄×C₁₁₃	—	2	1	no	—
177	C₄⋊C₄×C₁₁₃	—	2	2	no	—
178	C₄⋊C₄×C₁₁₃	—	2	2	no	—
179	C₄⋊C₄×C₁₁₃	—	2	2	no	—
180	C₄⋊C₄×C₁₁₃	—	2	2	no	—
181	C₄⋊C₄×C₁₁₃	—	2	2	no	—
182	C₄⋊C₄×C₁₁₃	—	2	2	no	—
183	C₄⋊C₄×C₁₁₃	—	2	2	no	—
184	C₄⋊C₄×C₁₁₃	—	2	2	no	—
185	C₄⋊C₄×C₁₁₃	—	2	2	no	—
186	C₄⋊C₄×C₁₁₃	—	2	1	no	—
187	C₄⋊C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
188	C₄⋊C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
189	C₄⋊C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
190	C₄⋊C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
191	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
192	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
193	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
194	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
195	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
196	C₂²⋊C₄×C₁₁₃	—	2	1	no	—
197	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
198	C₂²⋊C₄×C₁₁₃	—	2	1	no	—
199	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
200	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
201	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
202	C₂²⋊C₄×C₁₁₃	—	2	1	no	—
203	C₂²⋊C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
204	C₂²⋊C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
205	C₂²⋊C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
206	C₄²×C₁₁₃	—	2	1	no	—
207	C₄²×C₁₁₃	—	2	1	no	—
208	C₄²×C₁₁₃	—	2	2	no	—
209	C₄²×C₁₁₃	—	2	2	no	—
210	C₄²×C₁₁₃	—	2	1	no	—
211	C₄²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
212	C₄²×C₁₁₃	C₂²×C₄	1	2	yes	—
213	C₄²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
215	C₄²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
217	C₄²×C₁₁₃	C₂⁴	1	1	yes	characteristic
218	C₂³×C₁₁₃	—	2	1	no	—
219	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
220	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	Q₈×C₁₁₃	—	2	2	no	—
222	Q₈×C₁₁₃	—	2	4	no	—
223	Q₈×C₁₁₃	—	2	2	no	—
224	Q₈×C₁₁₃	—	4	2	no	—
225	Q₈×C₁₁₃	—	8	2	no	—
226	D₄×C₁₁₃	—	2	4	no	—
227	D₄×C₁₁₃	—	2	2	no	—
228	D₄×C₁₁₃	—	2	2	no	—
229	D₄×C₁₁₃	—	4	2	no	—
230	D₄×C₁₁₃	—	8	2	no	—
231	C₂×C₄×C₁₁₃	—	2	4	no	—
232	C₂×C₄×C₁₁₃	—	2	1	no	—
233	C₂×C₄×C₁₁₃	—	2	2	no	—
234	C₂×C₄×C₁₁₃	—	2	1	no	—
235	C₂×C₄×C₁₁₃	—	2	2	no	—
236	C₂×C₄×C₁₁₃	—	2	1	no	—
237	C₂×C₄×C₁₁₃	—	2	2	no	—
238	C₂×C₄×C₁₁₃	—	2	1	no	—
239	C₂×C₄×C₁₁₃	—	2	1	no	—
240	C₂×C₄×C₁₁₃	—	2	2	no	—
241	C₂×C₄×C₁₁₃	—	4	1	no	—
242	C₂×C₄×C₁₁₃	—	4	2	no	—
243	C₂×C₄×C₁₁₃	—	4	2	no	—
244	C₂×C₄×C₁₁₃	—	4	1	no	—
245	C₂×C₄×C₁₁₃	—	4	1	no	—
246	C₂×C₄×C₁₁₃	—	4	2	no	—
247	C₂×C₄×C₁₁₃	—	8	1	no	—
248	C₂×C₄×C₁₁₃	—	8	1	no	—
249	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
252	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
253	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
254	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₄×C₁₁₃	#131	1	4	yes	—
256	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
257	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
259	C₈×C₁₁₃	—	2	2	no	—
260	C₈×C₁₁₃	—	4	1	no	—
261	C₈×C₁₁₃	—	4	2	no	—
262	C₈×C₁₁₃	—	4	1	no	—
263	C₈×C₁₁₃	—	4	2	no	—
264	C₈×C₁₁₃	—	4	1	no	—
265	C₂²×C₁₁₃	—	2	1	no	—
266	C₂²×C₁₁₃	—	2	1	no	—
267	C₂²×C₁₁₃	—	2	2	no	—
268	C₂²×C₁₁₃	—	2	2	no	—
269	C₂²×C₁₁₃	—	2	2	no	—
270	C₂²×C₁₁₃	—	4	1	no	—
271	C₂²×C₁₁₃	—	4	1	no	—
272	C₂²×C₁₁₃	—	4	1	no	—
273	C₂²×C₁₁₃	#408	1	2	yes	—
274	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
275	C₄×C₁₁₃	—	2	2	no	—
276	C₄×C₁₁₃	—	2	1	no	—
277	C₄×C₁₁₃	—	2	2	no	—
278	C₄×C₁₁₃	—	2	1	no	—
279	C₄×C₁₁₃	—	2	1	no	—
280	C₄×C₁₁₃	—	2	2	no	—
281	C₄×C₁₁₃	—	4	1	no	—
282	C₄×C₁₁₃	—	4	2	no	—
283	C₄×C₁₁₃	—	4	1	no	—
284	C₄×C₁₁₃	—	4	2	no	—
285	C₄×C₁₁₃	—	4	1	no	—
286	C₄×C₁₁₃	#408	1	2	yes	—
287	C₄×C₁₁₃	C₂×#131	1	2	yes	—
288	C₄×C₁₁₃	#577	1	1	yes	characteristic
289	C₄×C₁₁₃	#578	1	1	yes	characteristic
290	#17469	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
291	C₂×C₁₁₃	—	2	2	no	—
292	C₂×C₁₁₃	—	4	2	no	—
293	C₂×C₁₁₃	—	8	1	no	—
294	C₂×C₁₁₃	C₂×#408	1	1	yes	characteristic
295	C₂×C₁₁₃	#2898	1	1	yes	characteristic
296	C₂×C₁₁₃	#2901	1	1	yes	characteristic
297	#3461	C₂×C₁₁₃	1	1	yes	characteristic
298	#2988	C₂×C₁₁₃	1	1	yes	characteristic, complemented
299	#2965	C₂×C₁₁₃	1	1	yes	characteristic, complemented
300	#1485	C₂×C₁₁₃	1	2	yes	complemented
301	#1483	C₂×C₁₁₃	1	2	yes	complemented
302	#1482	C₂×C₁₁₃	1	2	yes	complemented
303	#1481	C₂×C₁₁₃	1	2	yes	complemented
304	#1479	C₂×C₁₁₃	1	1	yes	characteristic, complemented
305	#1477	C₂×C₁₁₃	1	1	yes	characteristic, complemented
306	#1476	C₂×C₁₁₃	1	1	yes	characteristic, complemented
307	C₂×Q₈⋊C₈	C₂×C₁₁₃	1	1	yes	characteristic, complemented
308	C₁₁₃	#17469	1	1	yes	characteristic, direct product factor, Sylow
309	#544	C₄×C₁₁₃	1	1	yes	characteristic
310	#542	—	2	1	no	—
311	#542	C₄×C₁₁₃	1	2	yes	—
312	#541	—	2	1	no	—
313	#541	C₄×C₁₁₃	1	2	yes	—
314	#539	—	2	2	no	—
315	#537	C₄×C₁₁₃	1	1	yes	characteristic
316	#536	C₄×C₁₁₃	1	1	yes	characteristic
317	#536	C₄×C₁₁₃	1	1	yes	characteristic
318	#533	—	2	1	no	—
319	#533	C₂²×C₁₁₃	1	2	yes	—
320	#529	—	2	2	no	—
321	#529	—	2	1	no	—
322	#529	C₂²×C₁₁₃	1	2	yes	—
323	C₄×#41	C₂²×C₁₁₃	1	1	yes	characteristic
324	C₄×#41	C₂²×C₁₁₃	1	1	yes	characteristic
325	C₂×C₄×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
326	#446	—	2	1	no	—
327	C₈×Q₈	—	2	1	no	—
328	#436	—	2	1	no	—
329	#435	—	2	2	no	—
330	C₈×D₄	—	2	1	no	—
331	C₈×D₄	—	2	2	no	—
332	#431	C₂²×C₁₁₃	1	1	yes	characteristic
333	#431	C₂²×C₁₁₃	1	2	yes	—
334	#431	C₂²×C₁₁₃	1	1	yes	characteristic
335	#431	C₂²×C₁₁₃	1	2	yes	—
336	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	1	yes	characteristic
337	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
338	C₄×M₁₆	C₂²×C₁₁₃	1	2	yes	—
339	C₂×C₄×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
340	Q₈⋊C₈	C₂²×C₁₁₃	1	2	yes	—
341	Q₈⋊C₈	C₂²×C₁₁₃	1	2	yes	—
342	Q₈⋊C₈	C₂²×C₁₁₃	1	1	yes	characteristic
343	Q₈⋊C₈	C₂²×C₁₁₃	1	1	yes	characteristic
344	Q₈⋊C₈	C₂²×C₁₁₃	1	2	yes	—
345	Q₈⋊C₈	C₂²×C₁₁₃	1	2	yes	—
346	Q₈⋊C₈	C₂²×C₁₁₃	1	2	yes	—
347	D₄⋊C₈	C₂²×C₁₁₃	1	1	yes	characteristic
348	D₄⋊C₈	C₂²×C₁₁₃	1	1	yes	characteristic
349	D₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
350	C₂×#41	C₂×C₄×C₁₁₃	1	1	yes	characteristic
351	C₂×#41	C₂×C₄×C₁₁₃	1	1	yes	characteristic
352	C₂²×Q₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
353	C₂×M₁₆	—	2	2	no	—
354	C₂²×C₈	—	2	1	no	—
355	C₂²×C₈	—	2	1	no	—
356	C₂²×C₈	—	2	2	no	—
357	C₄⋊Q₈	—	2	1	no	—
358	C₄⋊Q₈	—	2	1	no	—
359	C₄⋊Q₈	C₂×C₄×C₁₁₃	1	2	yes	—
360	C₄⋊Q₈	C₂×C₄×C₁₁₃	1	2	yes	—
361	#126	—	2	2	no	—
362	#126	—	2	2	no	—
363	#126	—	2	2	no	—
364	#126	—	2	2	no	—
365	#125	—	2	2	no	—
366	#125	—	2	1	no	—
367	#125	—	2	2	no	—
368	#125	—	2	2	no	—
369	#125	C₂×C₄×C₁₁₃	1	2	yes	—
370	#124	—	2	1	no	—
371	#124	—	2	2	no	—
372	#124	C₂×C₄×C₁₁₃	1	2	yes	—
373	#123	—	2	2	no	—
374	#123	—	2	2	no	—
375	#123	—	2	2	no	—
376	#123	—	2	2	no	—
377	C₂²⋊Q₈	—	2	1	no	—
378	C₂²⋊Q₈	—	2	2	no	—
379	C₂²⋊Q₈	—	2	1	no	—
380	C₂²⋊Q₈	—	2	1	no	—
381	C₂²⋊Q₈	—	2	2	no	—
382	C₂²⋊Q₈	—	2	2	no	—
383	C₂²⋊Q₈	C₂×C₄×C₁₁₃	1	2	yes	—
384	C₂²⋊Q₈	C₂×C₄×C₁₁₃	1	2	yes	—
385	C₂²⋊Q₈	C₂×C₄×C₁₁₃	1	2	yes	—
386	#121	—	2	2	no	—
387	#121	—	2	1	no	—
388	#121	C₂×C₄×C₁₁₃	1	2	yes	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	—	2	2	no	—
392	C₄×Q₈	C₂×C₄×C₁₁₃	1	2	yes	—
393	C₄×Q₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
394	C₄×Q₈	D₄×C₁₁₃	1	1	yes	characteristic
395	C₄×Q₈	D₄×C₁₁₃	1	1	yes	characteristic
396	C₄×Q₈	C₂³×C₁₁₃	1	2	yes	—
397	C₄×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
402	C₄×D₄	D₄×C₁₁₃	1	1	yes	characteristic
403	C₄×D₄	D₄×C₁₁₃	1	2	yes	—
404	C₄×D₄	D₄×C₁₁₃	1	2	yes	—
405	C₄×D₄	D₄×C₁₁₃	1	1	yes	characteristic
406	C₄×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
407	#117	—	2	2	no	—
408	#117	—	2	1	no	—
409	#117	—	2	2	no	—
410	#117	C₂×C₄×C₁₁₃	1	1	yes	characteristic
411	#117	C₂×C₄×C₁₁₃	1	1	yes	characteristic
412	#117	C₂×C₄×C₁₁₃	1	2	yes	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	—	2	1	no	—
417	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
419	C₄⋊C₈	—	2	1	no	—
420	C₄⋊C₈	—	2	2	no	—
421	C₄⋊C₈	—	2	2	no	—
422	C₄⋊C₈	—	2	1	no	—
423	C₄⋊C₈	C₂³×C₁₁₃	1	1	yes	characteristic
424	C₄⋊C₈	C₂³×C₁₁₃	1	2	yes	—
425	C₄⋊C₈	C₂³×C₁₁₃	1	1	yes	characteristic
426	C₂²⋊C₈	—	2	1	no	—
427	C₂²⋊C₈	—	2	2	no	—
428	C₂²⋊C₈	—	2	1	no	—
429	C₂²⋊C₈	—	2	2	no	—
430	#97	—	2	2	no	—
431	C₄×C₈	—	2	1	no	—
432	C₄×C₈	—	2	1	no	—
433	C₄×C₈	—	2	2	no	—
434	C₄×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
435	C₄×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
436	C₄×C₈	C₂³×C₁₁₃	1	2	yes	—
437	#41	—	2	4	no	—
438	#41	—	2	4	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	2	no	—
441	C₂×Q₈	—	2	4	no	—
442	C₂×Q₈	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
443	C₂×Q₈	C₂²×C₄×C₁₁₃	1	2	yes	—
444	C₂×Q₈	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
448	C₂×D₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
449	C₂×D₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
456	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
459	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
461	M₁₆	—	4	4	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	4	2	no	—
469	C₂×C₈	—	8	1	no	—
470	C₂×C₈	—	8	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
485	C₄⋊C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
486	C₄⋊C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
487	C₄⋊C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
488	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
489	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
501	C₂²⋊C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
502	C₂²⋊C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	2	no	—
506	C₄²	—	2	2	no	—
507	C₄²	—	2	1	no	—
508	C₄²	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
509	C₄²	C₂²×C₄×C₁₁₃	1	2	yes	—
510	C₄²	C₂×D₄×C₁₁₃	1	1	yes	characteristic
511	C₄²	C₂×D₄×C₁₁₃	1	1	yes	characteristic
512	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
513	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
514	C₄²	C₂⁴×C₁₁₃	1	1	yes	characteristic
515	C₂³	—	2	1	no	—
516	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
517	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
518	Q₈	—	2	2	no	—
519	Q₈	—	2	4	no	—
520	Q₈	—	2	2	no	—
521	Q₈	—	4	2	no	—
522	Q₈	—	8	2	no	—
523	D₄	—	2	4	no	—
524	D₄	—	2	2	no	—
525	D₄	—	2	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	8	2	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	8	1	no	—
545	C₂×C₄	—	8	1	no	—
546	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
547	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
548	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
549	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
550	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
551	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
552	C₂×C₄	#131×C₁₁₃	1	4	yes	—
553	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
555	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
556	C₈	—	2	2	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	2	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	2	no	—
561	C₈	—	4	1	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	#408×C₁₁₃	1	2	yes	—
571	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
572	C₄	—	2	2	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	2	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	2	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	2	no	—
582	C₄	—	4	1	no	—
583	C₄	#408×C₁₁₃	1	2	yes	—
584	C₄	C₂×#131×C₁₁₃	1	2	yes	—
585	C₄	#577×C₁₁₃	1	1	yes	characteristic
586	C₄	#578×C₁₁₃	1	1	yes	characteristic
587	C₂	—	2	2	no	—
588	C₂	—	4	2	no	—
589	C₂	—	8	1	no	—
590	C₂	C₂×#408×C₁₁₃	1	1	yes	characteristic
591	C₂	C₁₁₃×#2898	1	1	yes	characteristic
592	C₂	C₁₁₃×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₁₃
socle	C₂²×C₁₁₃	C₂²×C₂²⋊C₄
prime radical	#537×C₁₁₃	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁₃ ◁ C₄×#41×C₁₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₁₃×#2988	C₂	semidirect
3. C₁₁₃×#2965	C₂	semidirect
4. C₁₁₃×#1485	C₂	semidirect
5. C₁₁₃×#1483	C₂	semidirect
6. C₁₁₃×#1482	C₂	semidirect
7. C₁₁₃×#1481	C₂	semidirect
8. C₁₁₃×#1479	C₂	semidirect
9. C₁₁₃×#1477	C₂	semidirect
10. C₁₁₃×#1476	C₂	semidirect
11. C₂×Q₈⋊C₈×C₁₁₃	C₂	semidirect
290. #17469	C₁₁₃	direct (N × H)
298. #2988	C₂×C₁₁₃	semidirect
299. #2965	C₂×C₁₁₃	semidirect
300. #1485	C₂×C₁₁₃	semidirect
301. #1483	C₂×C₁₁₃	semidirect
302. #1482	C₂×C₁₁₃	semidirect
303. #1481	C₂×C₁₁₃	semidirect
304. #1479	C₂×C₁₁₃	semidirect
305. #1477	C₂×C₁₁₃	semidirect
306. #1476	C₂×C₁₁₃	semidirect
307. C₂×Q₈⋊C₈	C₂×C₁₁₃	semidirect
308. C₁₁₃	#17469	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₁₃×#3461	2
C₁₁₃×#2988	2
C₁₁₃×#2965	2
C₁₁₃×#1485	2
C₁₁₃×#1483	2
C₁₁₃×#1482	2
C₁₁₃×#1481	2
C₁₁₃×#1479	2
C₁₁₃×#1477	2
C₁₁₃×#1476	2
C₂×Q₈⋊C₈×C₁₁₃	2
#17469	113

Subgroups — C113×#17469 #43285489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#17469 #43285489